Problem: What is the missing constant term in the perfect square that starts with $x^2+6x$ ?
Answer: Let $b$ be the missing constant term. Let's assume $x^2+6x+b$ is factored as the perfect square $(x+a)^2$. $\begin{aligned} (x+a)^2&=x^2+{2a}x+{a^2} \\\\ &=x^2+{6}x+ b \end{aligned}$ For the expressions to be the same, ${2a}$ must be equal to ${6}$, and ${a^2}$ must be equal to $ b$. From ${2a=6}$ we know that $a=3$. Now, from ${a^2=b}$ we know that $b=3^2=9$. Indeed, $x^2+6x+9$ is factored as $(x+3)^2$. In conclusion, the missing constant term in the perfect square that starts with $x^2+6x$ is $9$